Abstract
The existence of an idempotent generator for group codes or group ring codes in FqG plays a very important role in determining the minimal distance of the respective code. Some necessary and sufficient conditions for a group ring element to be an idempotent in F2Cn are investigated in this paper. The main result in this paper is the affirmation of the existence of finitely many basis idempotents which gives a full identification of all idempotents in every binary cyclic group ring F2Cn. All the basis idempotents in F2Cn are able to be found by partitioning the largest idempotent’s support.
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